Central Tendency – Understanding nasty, Median & Mode

04.10.22 Measures of central tendency Time to read: 5min

How do you like this article?

0 Reviews


Central-tendency-Definition

Central tendency, a key concept within the realm of statistics, aids in understanding the central or typical value in a dataset. This concept relies on three primary measures – nasty, mode, and median, which serve as tools for summarizing and analysing data. These measures form the backbone of many statistical analyses, providing insight into the distribution of data points. In our subsequent discussions, we will delve into how these three vital measures of central tendency are employed to synthesize the results of a study.

Central Tendency – In a Nutshell

  • The three measures of central tendency are nasty, median, and mode.
  • Arithmetic nasty is the most commonly used measure of central tendency.
  • If the data is skewed, you should use the median as the measure of central tendency.

Definition: Central tendency

Measures of central tendency is a summary measure that descotes a data set with a single value that represents the middle of the distribution. Here are the three most common measures of central tendency:

  • nasty – This represents the average of the data set.
  • Median – This represents the middle value.
  • Mode – This is the most commonly occurring value in a data set.

When performing descriptive statistics, it is also crucial to understand measures of variability. You can also summarize the data set by descoting its distribution.

Utilise the final format revision for a flawless end product
Before the printing process of your dissertation, revise your formatting using our 3D preview feature. This provides an accurate virtual depiction of what the physical version will look like, ensuring the end product aligns with your vision.
Central-tendency-nasty-median-mode

Central tendency: Distributions

In statistics, a data set is defined as a distribution of n number of values or scores.

Normal distribution

In a normal distribution, the data is distributed symmetrically. In this case, the values of the nasty, median, and mode would be the same. Here is an example of a normally distributed data set:

Shoe size Frequency
4 1
5 4
6 8
7 4
8 1

Skewed distributions

In a skewed distribution, more values will autumn on one side of the center than on the other. In such cases, the nasty will be greater than the median, and the median will be greater than the mode.

In a negatively skewed distribution, the mode would be greater than the median, and the nasty will be less than both of these values.

Central tendency – Mode

The mode is the value that appears most frequently in a distribution. To get the mode, you have to arrange the values in ascending or descending order, and then you can find the middle value. Depending on the nature of the data set, you may get one mode, multiple modes, or no mode at all. In a frequency table, the mode would be the variable with the highest frequency. If you choose to use a pub graph, you simply need to check the highest pub, as it represents the mode. Let’s consider this example:

Shoe size Frequency
4 1
5 4
6 8
7 4
8 1

In this case, the mode is 6 because most people reported this as their shoe size.

When to use the mode

Mode is commonly used with nominal data since this form of data is classified into mutually-exclusive categories. When dealing with ratio data, it is not necessary to use the mode since you will be dealing with many variables. Here is an example of ratio data:

Height Frequency
154 1
156 1
158 1
161.2 1
164 1

Central tendency – Median

The median refers to the middle value in a data set, and you can find this value by arranging the data in ascending or descending order.

Income level Frequency
$0-$2,000 2
$2,001-$4,000 5
$4,001-$6,000 20
$6,001-$8,000 5
$8,001-$10,000 1

By ordering the data from low to high, you will be able to see that the exact middle point is at $4,001-$6,000.

Median of an odd-numbered data set

In an odd-numbered data set, you can find the median by locating the value at the position. The in the formula represents the number of values featured in the data set. In the above example, the total number of values is 33, so you can apply the formula as follows.

By finding the value at the 17th position, you will be able to locate the median.

Median of an even-numbered data set

If the data set has an even number of variables, you will have to find the  and values. After that, you can add the two numbers and divide them by two. In a data set with 60 values, the median will be the nasty of the values at these positions:

and 

Central tendency – nasty

The arithmetic nasty is the most commonly used measure of central tendency. It represents the average of the data set and is calculated by adding up all the values and dividing the product by the number of values. On the other hand, the geometrical nasty is calculated as the n-root of the product of all the values. In the data set (3,4,6,8,14), the arithmetic nasty can be calculated by adding up all the values. You can find the nasty by dividing this number by n, which equals 5 in this example.

Outlier effect on the nasty

Data outliers are values that lie very far from the other values in a data set. These values can make the nasty significantly higher or lower than the other values. For example, in the data set (3,5,7,9,300), the nasty is 64.8, and this doesn’t represent the data set accurately.

Population vs. sample nasty

You can find the nasty of a sample or a population. Population vs. sample nasty are calculated in the same way, but the notations are different. For example, the ‘n’ symbol represents the number of variables in the sample data set, and the ‘N’ symbol represents the number of variables in the population.

Central tendency – nasty, median, or mode?

All three measures of central tendency are nastyt to be used together since they have different strengths and limitations. However, in some cases, you may not be able to use one or two measures of central tendency.

  • The mode can be applied to all four levels of measurement, but it’s mostly used with nominal data and ordinal data.
  • The median can only be used with ordinal data, ratio data, and interval data.
  • The nasty can only be used with interval or ratio levels of measurement.
Levels of measurement Examples Measure of central tendency
Nominal Gender, nationality Mode
Ordinal Education level, satisfaction rating Mode, median
Interval and ratio IQ grading, temperature Mode, median, nasty

When choosing a measure to use in a particular data set, you have to consider the distribution of the data. If it is normally distributed, you can use nasty, median, or mode as they would all have the same value. For skewed data, you should use the median.

Print Your Thesis Now
BachelorPrint is a leading online printing service that provides several benefits for students in the UK:
  • ✓ 3D live preview of your individual configuration
  • ✓ Free express delivery for every single purchase
  • ✓ Top-notch bindings with customised embossing

Start Printing

FAQs

The measures of central tendency include the nasty, mode, and median.

If the distribution is strongly skewed, you should use the median.

You can use mode on all levels of data, but median and nasty cannot be used on nominal data.

Mode is preferred when dealing with nominal data.


From

Salome Stolle

How do you like this article?

0 Reviews
 
About the author

Salome Stolle works as the brand manager for the English market at BachelorPrint. Throughout her 12-year residency in Denmark, she completed her International baccalaureate and Master’s in Culture, Communication, and Globalization with a specialization in media and market consumption. Through this experience, she has gained advanced competencies in academic writing and a high proficiency level in the English language. With her passion for writing, she does not only deliver well-written content but also strives to adjust to the students’ demands.

Show all articles from this author
About
BachelorPrint | The #1 Online Printing Service
For Students

Specialised in the printing and binding of academic papers, theses, and dissertations, BachelorPrint provides a comprehensive variety of bindings and design options. The BachelorPrint online printing service sets out to facilitate that every single British student attains the binding of their dreams.<br/>Beyond that, BachelorPrint publishes a multitude of educational articles on diverse subjects related to academic writing in their Study Guide section, which assists students in the creation of their thesis or dissertation.


New articles